Linked Questions

37
votes
2answers
5k views

Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`?

Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schrödinger) equation, for the free particle propagation of an initial wavepacket. ...
50
votes
2answers
3k views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
7
votes
2answers
2k views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
34
votes
2answers
10k views

Logarithmic scale in a DensityPlot and its legend

I was recently faced with the task of creating a DensityPlot with a logarithmic colour scale, and with providing it with an appropriate legend. Since I could not find any resources to this effect on ...
6
votes
1answer
2k views

Circular membrane vibration simulation

I'm new in Mathematica and I'm trying to simulate the vibration of a circular membrane for math project but I don't even know how to start. The wave equation describes the displacement of the ...
20
votes
1answer
788 views

Eigenfunctions of the Laplacian on an arbitrary mesh

So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge). Mostly because I figured an ...
9
votes
1answer
249 views

Gaining precision/accuracy with NDEigenvalues

See further down for an important note Background I study (one component of) the semi-classical Pauli operator, $$ P_h=-h^2\Delta+ih(-y,x)\cdot\nabla+\frac{x^2+y^2}{4}-h. $$ For this particular ...
3
votes
2answers
160 views

Schrödinger equation for a hydrogen atom and lack of memory

I'm trying to solve the Schrödinger equation for a hydrogen atom in the Cartesian coordinate system. This is my code ...
1
vote
2answers
501 views

Comparing analytical solution with numerical solution of Helmholtz equation in a unit square

I am just learning PDE, and I am interested to compare analytical solution with numerical solution of Helmholtz equation in a unit square with zero boundary condition. I am not sure if it possible. ...
6
votes
1answer
100 views

NDEigenvalues complains not Hermitian with large dimension differential operator

The following snippet calculates eigenvalues and eigenfunctions of a null operator (just as an example): ...
3
votes
1answer
420 views

Finding eigenvalues for Laplacian operator for 3D shape with Neumann boundary conditions

I've just begun to use the Mathematica so my question may seem to be naive. To get a solution for my problem I looked at the example provided in help. ...
5
votes
1answer
133 views

How to control DifferenceOrder in NDEigenvalue for an ODE?

I am trying to solve the eigenvalue problem of a 1st-order ODE system using NDEigenvalue. It should be finite difference method for ODE. And I want to tune the the ...
4
votes
0answers
264 views

Spectral problem for differential vector operator (calculation of EM field in a cavity)

I know that mathematica has a DEigensystem and NDEigensystem which allow one to find eigenfunction and ...
1
vote
0answers
170 views

Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]

I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...